ISOMetrisches

ISOMetrisches is a term used to refer to the German adjective isometrisch, meaning isometric in English. In scientific and technical contexts, it describes properties or methods that preserve measurement distances, rather than scale or perspective.

In mathematics, an isometry is a function between metric spaces that preserves distances: for all points x,y, d(f(x), f(y)) = d(x,y). Isometries include translations, rotations, reflections, and their combinations. They preserve lengths, angles, and shapes up to congruence.

In graphics and technical drawing, an isometric projection is a method to represent three-dimensional objects on a two-dimensional plane with equal scaling along three axes, commonly at 120 degrees apart. It produces a pictorial without true perspective, helping to visualize structure.

The term also appears in crystallography and chemistry as the "isometric" (cubic) crystal system, where unit cell axes are equal and angles are right angles, describing high-symmetry crystal structures. In anatomy or medicine, "isometric" can describe equal-length contractions of muscles, though more specific terms may be used.

Etymology: from Greek isos "equal" and metron "measure." The term is used in multiple disciplines, often with the root meaning of preserving equality of distances or scales.